This sounds like small intestine bacterial overgrowth (SIBO) to me. The antibiotic of choice for treatment is Xifaxan, but with stubborn cases you usually do need to do the close to zero carb diet for a while I've read about some success with treating SIBO using the FODMAP diet lately as well.
There's a breath test for SIBO -- it seems a lot of GIs don't want to bother doing it, and would rather just have you take Xifaxan and if that helps they'll call it SIBO. I don't know, if I were potentially embarking on another course of antibiotics and possibly a really strict diet, I would probably want the test first. I've done the test myself in the past and it was pretty painless and it did confirm SIBO. I would ask your GI about it.